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Since its inception in 2009, Bitcoin has increasingly gained main stream attention from the general population to institutional investors. Several models, from GARCH type to jump-diffusion type, have been developed to dynamically capture the price movement of this highly volatile asset. While fitting the Gaussian and the Generalized Hyperbolic and the Normal Inverse Gaussian (NIG) distributions to log-returns of Bitcoin, NIG distribution appears to provide the best fit. The time-varying Hurst parameter for Bitcoin price reveals periods of randomness and mean-reverting type of behaviour, motivating the study in this paper through fractional Ornstein–Uhlenbeck driven by a Normal Inverse Gaussian Lévy process. Features such as long-range memory are jump diffusion processes that are well captured with this model. The results present a 95% prediction for the price of Bitcoin for some specific dates. This study contributes to the literature of Bitcoin price forecasts that are useful for Bitcoin options traders.

A Monte Carlo Approach to Bitcoin Price Prediction with Fractional Ornstein–Uhlenbeck Lévy Process